Dielectrics are essential components in modern electronics and electric systems. When a sufficiently high voltage is applied on a layer of a dielectric, the dielectric will breakdown electrically. The breakdown limits the electrical energy density of the dielectric. We show that constraining the deformation of soft dielectrics can greatly enhance their breakdown electric fields and thus increase their electrical energy densities. The mechanical constraints suppress electromechanical instabilities, a major cause for electrical breakdowns in soft dielectrics.